question

Which statement is true about the diagram?

answer

âˆ BEA â‰… âˆ BEC

question

Segment AB is congruent to segment AB.
This statement shows the _____ property

answer

reflexive

question

Given that RT â‰… WX, which statement must be true?

answer

RT + TW = WX + TW

question

A two-column proof

answer

contains a table with a logical series of statements and reasons that reach a conclusion.

question

Given that D is the midpoint of AB and K is the midpoint of BC, which statement must be true?

answer

AK + BK = AC

question

What is the missing justification?

answer

transitive property

question

Given that âˆ CEA is a right angle and EB bisects âˆ CEA, which statement must be true?

answer

mâˆ CEB = 45Â°

question

Given that âˆ ABC â‰… âˆ DBE, which statement must be true?

answer

âˆ ABD â‰… âˆ CBE

question

Which statement is true about the diagram?

answer

K is the midpoint of AB.

question

Given that BA bisects âˆ DBC, which statement must be true?

answer

mâˆ ABD = mâˆ ABC

question

Name the three different types of proofs you saw in this lesson. Give a description of each.

answer

One type of proof is a two-column proof. It contains statements and reasons in columns. Another type is a paragraph proof, in which statements and reasons are written in words. A third type is a flowchart proof, which uses a diagram to show the steps of a proof.

question

Which property is shown?
If mâˆ ABC = mâˆ CBD, then mâˆ CBD = mâˆ ABC

answer

symmetric property

question

EB bisects âˆ AEC.
What statements are true regarding the given statement and diagram?

answer

âˆ CED is a right angle.
âˆ CEA is a right angle.
mâˆ CEB = mâˆ BEA
mâˆ DEB = 135Â°

question

Given: mâˆ ABC = mâˆ CBD
Prove: BC bisects âˆ ABD.
Justify each step in the flowchart proof.

answer

A: given
B: definition of congruent
C: definition of bisect

question

Describe the main parts of a proof.

answer

Proofs contain given information and a statement to be proven. You use deductive reasoning to create an argument with justification of steps using theorems, postulates, and definitions. Then you arrive at a conclusion.

question

Given: EB bisects âˆ AEC.
âˆ AED is a straight angle.
Prove: mâˆ AEB = 45Â°
Complete the paragraph proof.
We are given that EB bisects âˆ AEC. From the diagram, âˆ CED is a right angle, which measures __Â° degrees. Since the measure of a straight angle is 180Â°, the measure of angle ______ must also be 90Â° by the _____. A bisector cuts the angle measure in half. mâˆ AEB is 45Â°.

answer

90
AEC
angle addition postulate

question

Given: âˆ ABC is a right angle and âˆ DEF is a right angle.
Prove: All right angles are congruent by showing that âˆ ABC â‰…âˆ DEF.
What are the missing reasons in the steps of the proof?

answer

A: definition of right angle
B: substitution property
C: definition of congruent angles

question

Identify the missing parts in the proof.
Given: âˆ ABC is a right angle.
DB bisects âˆ ABC.
Prove: mâˆ CBD = 45Â°

answer

A: given
B: measure of angle ABC = 90
C: angle addition postulate
D: 2 times the measure of angle CBD = 90

question

Given: mâˆ A + mâˆ B = mâˆ B + mâˆ C
Prove: mâˆ C = mâˆ A
Write a paragraph proof to prove the statement.

answer

We are given that the sum of the measures of angles A and B is equal to the sum of the measures of angles B and C. The measure of angle B is equal to itself by the reflexive property, so you can subtract that measure from both sides of the equation. Now the measure of angle A equals the measure of angle C. By the symmetric property, this means the measure of angle C equals the measure of angle A.